Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 10

10 Opening champagne. In a bottle of champagne, the pocket of gas (primarily carbon dioxide) between the liquid and the cork is at pressure of \(p_i = 4.00 \text{ atm}\). When the cork is pulled from the bottle, the gas undergoes an adiabatic expansion until its pressure matches the ambient air pressure of \(1.00 \text{ atm}\). Assume that the ratio of the molar specific heats is \(\gamma = \frac{4}{3}\). If the gas has an initial temperature \(T_i = 5.00^\circ\text{C}\), what is its temperature at the end of the adiabatic expansion?